If that's how Newton communicated I'm quite glad we adopted Leibniz' notation.
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Owned by Bernoulli! That's sad...
Agree that Sir Isaac's notation sucked. Leibniz's gang did give him credit occasionally, though. You do remember the "Tanquam ex ungue leonem" -story?
Newton's notation is not only horrible. It is downright unclear thinking. I enjoy retelling the joke that the Lucasian Professor of Mathematics fails at basic mathematics.
Basically, Newton's notation only deals with derivatives with respect to time, so dy/dx becomes y dot over x dot. 2nd derivatives and so on become monstrous and that is exactly why he did not bother to do much of them.
Other than the being poorly thought out, the notation is incapable of generalisation and comparisons. Because Newton's failed at basic maths, he was unable to see that Newton's 3 Laws are all the same law -- it is easy to see how the 1st law is a special case of the second, but someone also proved that the 3rd law is a direct consequence of the 2nd too.
If being long winded is not bad enough, Newton's 2nd law, which implies the conservation of momentum, immediately implies the conservation of energy, a point of contention that Newton vehemently objected against, causing the entire Physics community to have to wait 200+ years for thermodynamics. (Thermodynamics depends heavily on conservation of energy.)
Leibniz's notation, on the other hand, clearly shows relationships and is generalisable. Not only is his method clear, he thought out the problems in greater detail too, and that leads to his Leibniz Integral Rule, which is too beautiful to talk about here.
It is very sad, because Leibniz clearly looked up to Newton before the incident. Imagine the hero you idolise backstabbing you. Not a nice thought.
I'm not so sure that Newton's 3 law are logically identical...
If that was the case, why haven't the science community sumarized it to more basic laws? The way I see it goes something like this:
First Law: It allows us to determine wich reference is inertial (with respect to another inertial frame). If the second frame has a chaging velocity its not inertial.
Second Law: F = m*a. Describes how a body react to a force. Note this is not a definition, because forces arrise from interaction and could change the position of a particle in any other way, rather than being proportional to the 2nd derivative.
Third Law: Well...there isn't even much to say here...While I agree that sometimes 1st law may seen like a direct consequence of 2nd law, this one for me has nothing to do at all. I don't see why a Universe where there was no reaction couldn't exist and still satisfie 2nd law.
(sorry for many mistakes, not native in english)
The problem is that it already had been simplified -- nobody talks about anything other than Newton's 2nd law these days. Yet, the scientific community is not so interested in axiomatisation.
If you are interested in it, Newton's 1st Law is a paradigm change, which needs the 2nd Law to give quantitative answers. Once you apply no force in the 2nd Law, it immediately implies the 1st Law. The 2nd Law is originally given as F=dp/dt -- it was, in no way, written in the Principia as F=ma.
Then, someone proved that, if you consider 2 objects interacting, even with different masses, the 2nd Law will cause the 3rd Law to hold. So the 3rd Law is also dependant on the 2nd Law. Yuck. The 3rd Law is still useful, though, because it is capable of inducing the right ideas about forces when teaching.
The 2nd law is pretty intuitive, whereas the 3rd law is probably a surprise to most people when they learn it. It is certainly possible to imagine a world in which the 2nd law holds, but not the 3rd law, and most people probably think they live in a world like that even today.
So I personally would not belittle Newton for putting that out as a law, even if you can derive one from the other with our more developed viewpoints. I have noticed that begining Physics courses in continental Europe often do not teach Newton's laws, and that Anglo-Saxen courses always do. So there is a cultural bias here too.
no, newton's second law does not imply the third law. neither do newton's laws imply conservation of energy (for example, friction is allowable without giving off heat, until you have the explanation of heat as energy of small particles, which they didn't have until centuries later). The first law is a special case of the second, but newton liked having three laws because he like the number 3, and because he developed them in that order.
Still think 2nd does not imply in the first one. The second one holds only in a inertial frame of reference, and the first law is exactly defining what is a inertial reference. Of course, the first law needs another frame of reference to begin with, wich Newton tougth to be the "absolute space" and that is exactly the whole problem with his theory, isn't it? I'm not discussing if they are tottaly right, but if all of them are needed.
Not to mention the problem of defining mass, which newton definied as density times volume, but he never comes back to density. Without a definition of mass the second law breaks down, which implies that Newtonian mechanics is defined with respect to common sense, which I guess is the best way to view it. Axiomitazation of physics is not really relevant to any physicsist except for some rare type, I guess.
If you want more Newton humor (no Leibniz yet), check out the Scientific Revolution theme of strips at Irregular Webcomic.
Do people talk like this on Facebook? I haven't used FB in a few months, but when I was there, the grammar was usually a lot better than this texting gibberish.
The grammar on Facebook depends a great deal on who your friends are.
Was the horribly-wrong aspect ratio of Newton's picture a subtle gibe at how people who ignore grammar and spelling also seems to invariably not have eyes, or was it coincidence?
the case for non-Euclidean Geometry is even worse: the story is that Gauss figured it out, but was afraid to publish. When Janos Bolyai dared to publish his work, though, Gauss's response--that he had figured it out 30 years earlier--seems to have crushed Bolyai. And yet Bolyai had the much greater courage to publish as an unknown. Gauss comes across much as Newton does here.
I remembered watching the issue on BBC and IIRC, Bolyai was in the war when he had the time to think of the topic. When he received the letter from Gauss, he was so devastated that he committed suicide. Gauss was praising him to his peers, but decided that tough love was warranted. His misjudgement brought himself some sadness too.
While this comic is hilarious, what is even funnier are the comments.